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Progression of technology for quantum control or: jumping and drifting of NV centres

Difficulty

Technological sophistication is a cornerstone of our society. Apart from a few outstanding examples, technology has always advanced towards a new echelon, which in turn enabled further advance. Whether one investigates the height of the tallest skyscrapers, or the timeline from the first transistor to today’s computers, the principle remains the same: inventions are being made with increasingly faster strides. Of course this trend should hold true for our favourite qubit! Along these lines I will delve into a technological aspect of my favourite qubit: the nitrogen-vacancy (NV) centre in diamond.

A nitrogen-vacancy centre (red and transparent spheres) in the crystal lattice of diamond (black). Adapted from B. Hensen, PhD thesis.

What kind of qubit is the NV centre? It is a magnetic and optically-active crystal defect in diamond that consists of one vacant lattice site and an adjacent nitrogen atom. Specifically its optical-activity make the NV centre one of the candidate-systems for solid-state based quantum communication. Any form of quantum communication requires the distribution of entanglement (see Jeremy’s blogpost on teleportation). In the case of NV centres one would need to create entanglement between distant NVs, situated in different diamonds. Photons are ideal information carriers for long distances and are therefore used as mediators of entanglement. Thus by observing the optical activity of both partaking NVs one can create entanglement. Just like most operations in quantum technology, exquisite knowledge of the two systems is required to achieve this feat. Quantum mechanics requires that the emission of both partaking NVs is indistinguishable in all properties. Specifically the energy difference between the ground state and the optically excited state of the NV centre is imprinted onto the emission in terms of frequency.

This is where we encounter our technological aspect: the energy levels of NVs (and therefore the emission frequency) are influenced by the local electrical charge environment, that is constantly fluctuating. The charge environment consists of many more defects (e.g. a single vacant lattice site), that can host a varying number of electrons. Thus other defects in the vicinity of the NV give rise to changing electric fields. Fluctuating frequencies pose a problem: no entanglement without a stable/known emission frequency! An early idea that showed immediate success was to stick the NV in a capacitor and apply voltages to shift the emission frequency. But how do we identify the correct voltage level in a quick manner and mitigate any frequency drifts?

Let us have a look at the increasingly sophisticated techniques scientists came up with to solve this problem of emission frequency stabilization. The first logical step for anyone trying to understand a new problem is to garner experience and then utilize this experience to come up with a better solution. For the first experiments that entangled distant NVs, scientists sat down and tuned the applied voltages by hand to keep the two NVs on resonance. One could compare this to a very tedious, ungratifying and long-winding computer game (trust me, I have been in this situation). Yet, this technique is easy to realize, requires minimal technological overhead (the work force of a PhD student) and can be implemented immediately. However scaling our network of communication would require roughly one PhD per NV centre and would herald the return to the quantum version of telephone switchboards from the beginning of the 20th century. “Please hold the line while our operator searches for the frequency of your NV. Thank you for your patience.”, could be an announcement in the queue of quantum call centers when using this tech.

While tuning the emission by hand, we have learned quite a few things. The drift in frequency is dominated by two processes. First, slow and incremental changes of the charge environment cause a slow drift of the emission frequency over seconds. Second, on rare occasions there are large changes in emission frequency which occur rapidly (and are hence called jumps). Both processes can be attributed to the filling and emptying of charge traps that are far away from (slow drift) or close (jumps) to the NV. Slow variations are easier to handle than fast processes and can be treated with a slow feedback loop derived from control theory. This advance already reduces the required attention, makes the scientist focus on the frequency jumps that occur every other fifteen minutes and enables more difficult experiments (feedback loops do not tire and are generally better at keeping things stable).

During the next round of sophistication the scientist observes his or her own behaviour when a jump occurs and takes notes. He should ask himself a few questions: How do I detect that a jump occurred? How do I find the emission frequency again (e.g. via a large sweep of the applied voltage)? All of these considerations can be crafted together into a decision flow chart for a computer to find the frequency back automatically. The scientist thus emulates himself via a computer as a first approximation to find the appropriate automation process. Complex questions have the drawback that they require a lot of input parameters to make the right decision. The same holds for our frequency jumps: it turns out that each NV centre is different and requires slightly altered flow charts to obtain full automation.

The different levels of sophistication and control illustrated

Of course the next logical step is the automation of the parameter search for our flow charts. Or alternatively, the use of more flexible (but also more complicated) techniques from machine learning to replace the flow chart entirely. The reasoning here is: if a human can recognize patterns in these frequency jumps then a computer can do so as well and probably with a higher efficiency.

You see that there are multiple ideas out there to further improve. Implementing these will surely lead to further ideas and progress. Keep in mind that this little history of NV centre stabilization took place over the last three years. Within this time frame we almost went from manual control to full automation. Let this be an example for the progression of one of the many aspects of quantum technologies. I am sure that there is more to come.

Norbert works on the realization of diamond-based quantum networks. Besides being a professional NV tamer he enjoys food, bouldering and outdoor activities. He can do a kickflip.